A new class of modules for Toroidal Lie Superalgebras

TL;DR

This paper introduces a broad new class of modules for toroidal Lie superalgebras, extending the understanding of their structure and representations, including cases where G is a simple finite-dimensional Lie algebra.

Contribution

It constructs a large class of modules for toroidal Lie superalgebras, generalizing previous work to include cases with simple finite-dimensional Lie algebras.

Findings

Constructed a new class of modules for toroidal Lie superalgebras.

Extended the theory to include cases where G is a simple finite-dimensional Lie algebra.

Provided a framework for further exploration of representations of toroidal Lie superalgebras.

Abstract

In this paper we construct a large class of modules for toroidal Lie superalgebras. Toroidal Lie superalgebras are universal central extension of G tensor A where G is a basic classical Lie superalgebra and A is a Laurent polynomial ring in sevaral variables. The case where G is simple finite dimensional Lie algebra is included.